To have a big pool for recombinations, inbreeding is to be avoided and populations must be big enough.
IIRC that's not completely true. In mammal females, there is competition at the chromosome level to determine which member of each pair will end up in the first polar body (which is discarded) and which one ends up in the secondary oocyte (which then splits up to become the ovum and the secondary polar body).
So, ignoring mutations, the next generation gets a never before seen chromosomes that are a puzzle of the chromosomes of the mother and another never before seen chromosomes that are a puzzle of the chromosomes of father.
I still can't find how common is the crossover, but in one link I got about 70 crossovers during the formation of the egg (with a lot of variations), that is approximately 3 crossovers per chromosome. I guess the crossover rate for the sperm is similar.
There is an exception with the X and Y chromosomes in males, that can't crossover, so the Y chromosome is inherited without crossovers, and it's much easier to track the male ancestor line in the Y chromosome. See https://en.wikipedia.org/wiki/Y-chromosomal_Adam
Like a virus that doesn’t need a penetration mechanism because it’s literally Trojan horsed into the egg.
A virus without a penetrator is basically like a cassette tape of DNA.
Derpy egg plays random cassette tape, baby’s DNA is... well the books are cooked as they say. Traits, emerge.